index.m

%% Initialize
clear;
close all;

%% Define variables and functions
% cost function J has defined as matlab function
% J(x) = 3*x.^2 + 0.5*x.^3 - 40*x +40*cos(pi*x);
x = 0:0.1:10;
J = Jx(x);
figure(1);
plot(x,J)
grid minor;
title('The cost function');
xlabel('x');
ylabel('J(x)');

% Consider the word length 8-bit. hence 255 contization levels
% bin = numbConv(x) - converts double variables into binary string
% x = binNumbInv(bin) - converts binary string into double value

numOfPop = 8;

pop = round(rand(1,numOfPop)*10,1);     % generate initial population

stop_val = 10;      
ittr_count = 0;
min_variance = 0.012;                   % minimum variance for stop itterations
while(stop_val>min_variance)
    figure(1);
    plot(x,J)
    Jo = Jx(pop);
    hold on;
    grid minor;
    title('Genetic Algorithem');
    xlabel('x');
    ylabel('J(x)');

    plot(pop,Jo,'rv','MarkerSize',5,'LineWidth',2);
    hold off;
    
    % Meting pool
    csf = costF(Jo,'min');
    
    prob_weight = csf/sum(csf);
    
    % sort according to probability
    [b,I] = sort(prob_weight,'descend');
    % Roulet wheel mechanism
    raoletNum = round(rand(1,numOfPop)*(numOfPop-1) + 1);
    % selection
    mating_pairs_pop = pop(I);
    selected_pop = mating_pairs_pop(raoletNum);

    % cross-over
    new_pop = zeros(1,length(selected_pop));    % array for store new population

    for p = 1:2:length(selected_pop)
        mother = selected_pop(p);
        father = selected_pop(p+1);

        mother_bin = numbConv(mother);
        father_bin = numbConv(father);

        crossover_point = 1 + round(rand(1,1)*5); % crossover will happen binary locations 1 to 5

        mother_bin_new = [ mother_bin(1:crossover_point) father_bin(crossover_point+1:end)];
        father_bin_new = [ father_bin(1:crossover_point) mother_bin(crossover_point+1:end)];

        new_pop(p) = binNumbInv(mother_bin_new);
        new_pop(p+1) = binNumbInv(father_bin_new);

    end

    intermediate_pop = [pop new_pop];

    % Mutuation
    intermediate_Jo = Jx(intermediate_pop);
    intermediate_csf = costF(intermediate_Jo,'min');
    intermediate_csf_sort = sort(intermediate_csf,'descend');
    pop = intermediate_csf_sort(1:length(intermediate_csf_sort)/2); % remove less costie values
    
    stop_val = var(pop);            % Stopping criteria defined as lesser variance
    ittr_count = ittr_count + 1 ;
    pause(0.15)
end

fprintf('Local Minima : %.4f found in %d itterations\n',min(costF(Jx(pop),'min')),ittr_count);